The Complexity of Causality and Responsibility for Query Answers and non-Answers.
Abstract
An answer to a query has a well-defined lineage expression (alternatively
called how-provenance) that explains how the answer was derived. Recent work
has also shown how to compute the lineage of a non-answer to a query. However,
the cause of an answer or non-answer is a more subtle notion and consists, in
general, of only a fragment of the lineage. In this paper, we adapt Halpern,
Pearl, and Chockler's recent definitions of causality and responsibility to
define the causes of answers and non-answers to queries, and their degree of
responsibility. Responsibility captures the notion of degree of causality and
serves to rank potentially many causes by their relative contributions to the
effect. Then, we study the complexity of computing causes and responsibilities
for conjunctive queries. It is known that computing causes is NP-complete in
general. Our first main result shows that all causes to conjunctive queries can
be computed by a relational query which may involve negation. Thus, causality
can be computed in PTIME, and very efficiently so. Next, we study computing
responsibility. Here, we prove that the complexity depends on the conjunctive
query and demonstrate a dichotomy between PTIME and NP-complete cases. For the
PTIME cases, we give a non-trivial algorithm, consisting of a reduction to the
max-flow computation problem. Finally, we prove that, even when it is in PTIME,
responsibility is complete for LOGSPACE, implying that, unlike causality, it
cannot be computed by a relational query.
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